Firstly, I agree that you seem to be doing an incredible job at keeping yourself motivated to try new things and to find work. It's always difficult to offer advice under these circumstances, as there are so many questions to ask you!
I think that you need to work out what you're able to commit to, given the constraints that you have on your time, with the children, and with your health issues. Don't try to take on too much as you will only feel worse if things don't work out. Try to focus on what you are able to do, rather than what you're not.
What are your interests? What jobs have you enjoyed most previously - what was it about the job that was so enjoyable? Was it the tasks you were doing, or the people you worked with, or the fact that you were learning new skills? It might be that you can use your hairdressing and beautician skills in a low-key, low commitment way, maybe by volunteering at a local nursing home or hospital. Or maybe you could stay in the environment that you have enjoyed (beauty industry) but in a different role - how would you feel about working as a receptionist in a beauty salon? Even by working or volunteering for a few hours a week, you will begin to get some structure to your week, regular contact with other people, and you will begin to build your confidence up. It will give you some time to spend thinking about what you want to do next, and maybe taking on some kind of study programme when your stress levels have reduced a bit. Little steps.
There is a great website: http://www.do-it.org.uk which has masses of volunteering opportunities registered, many of them only looking for a few hours a week. This could be a great starting point for you, if you are able to work voluntarily for a while.
If you are looking to earn some money as well, but don't want to commit to working for someone else, then there are businesses that you can sign up to where you can work from home, e.g. Phoenix Trading, selling greetings cards etc. The advantages are that you are selling a ready-made product, so you don't have to come up with a 'big idea' for a new business, and you can certainly work around the children. However, if you do find this kind of option appealing, please do consider the investment that you have to make up front, the number of other sellers of the same product in your area, and how comfortable you are with sales. You need to sell a lot of product to make any money. Talk to other traders before you commit, maybe attend an event that they run so you can see how it works in practice before you commit to anything yourself.
I'm a big believer in trying a few things out in a low-key way before making a decision. If you can come up with a shortlist of three or four options that are appealing to you, then start something really small towards that goal. For example, if teaching appeals to you, start with reading a trade magazine aimed at teachers - how does it feel to read it? is it exciting? Does it make you want to find out more? If so, try volunteering (maybe at a different school) in some capacity, then maybe look at a part-time teaching assistant role, then consider further training if you are really enjoying it and feel confident about the next steps. If you're interested in working in the beauty trade again, try and research the different roles available that might suit your current circumstances. Trade magazines, local papers, local area magazines etc are a great place to start to generate some ideas.
I don't know what your financial circumstances are and whether you have immediate need to be earning. If you have some time, it could be useful to try to get some current work experience. It's not just school leavers who do this - it is becoming more common amongst people who are looking to change or reestablish a career later on in life too. Some businesses may offer a low wage, others may not. But an up to date reference and recent experience within a business on your CV could make a huge difference in helping you to get a job further down the track.
You've come a long way in a very short space of time. Take it steadily, and use the time that you have while your children are at school to try to build your own health and well-being too - this could have an enormous impact on managing your stress levels. Maybe try a low impact exercise class at your local health centre - again this could add structure to your week and give you some interaction with a new group of people.
There's lots of ideas here, and only you will know if any of them are likely to be feasible for you. Please do let us know how you get on, or if we're way off track, let us know some other details about your situation and we can try to help more.
Take care, and really good luck. You're due a break...